Federal lawmakers and state officials are stepping up pressure on insurers to allow consumers whose coverage has been canceled in response to the health overhaul to keep their policies beyond the end of the year.

On Tuesday, one of the largest regional health plans in the nation, Blue Shield of California, said it would relax its stance on terminated policies for about 115,000 people after state regulators demanded it do so. Customers now will have until March to decide which plan to choose for 2014, a three-month...